Sensors having a sensor mass suspended by a spring suspension are well known. For instance, accelerometers and seismometers measure acceleration by measuring the deflection of an elastically supported proof mass. The sensitivity and bandwidth of such sensors are determined by the sensitivity and bandwidth of the motion detection electronics, the spring constant of the elastic support, and the value of the proof mass. Given wide bandwidth electronics, the sensor system bandwidth is determined by the mechanical resonance frequency of the spring-supported proof mass according to the equation: EQU 2.pi.f.sub.R =(k/m).sup.1/2 ( 1)
wherein:
f.sub.R =resonance frequency
k=spring constant
m=mass
At and below this frequency the sensitivity of the mechanical system is at a maximum. Above f.sub.R the sensitivity of the system falls inversely proportonal to the square of the frequency. However, the sensitivity of the mechanical system is also inversely proportional to f.sub.R for frequencies below f.sub.R. Therefore, the selection of f.sub.R by design of the mechanical structure is critical for determining the useful operating range of the sensor. In particular, it is clear that the sensor may not be optimized for wide bandwidth and high sensitivity simultaneously. Also, many seismometer, accelerometer and other sensor systems require large proof masses, and large sensor volume for adequate sensitivity.
In this respect and in general, sensitivity has continued to be a problem. For instance, temperature variations, non-linearity of suspension springs, overdrive, and other factors, all have contributed to significant sensitivity variations or degradations.
A linearizing scheme has been proposed by Felix Rudolf et al, in an article entitled SILICON MICROACCELEROMETER, Sensors and Actuators 4, 191 (1983). That article proposes an electrostatic force balancing accelerometer system in which a closed feedback loop arrangement restores the mass and thereby its spring suspension to a quiescent position at which the spring suspension has its quiescent spring constant. The advantage which a reduced spring constant would provide is thus lost in that approach.
Electrostatic force feedback is also used in accelerometers disclosed by Widge Henrion et al, in an article entitled WIDE DYNAMIC RANGE DIRECT DIGITAL ACCELEROMETER, and by Diederik W. de Bruin et al, in an article entitled SECOND-ORDER EFFECTS IN SELF-TESTABLE ACCELEROMETERS, both Technical Digest, IEEE Solid-State Sensor and Actuator Workshop, IEEE Catalog 90CH2783-9 (1990).
That article mentions that as the electrostatic force increases, the restoring force of the spring suspension is no longer able to counter the electrostatic force, causing the mass to move until it rests against its over-force stops, once the mass has traveled about half of the gap spacing. The mass is thus held by the electrostatic force and can only be released from such hold if the electrostatic voltage is reduced to the point where the restoring force of the spring suspension exceeds the electrostatic force again.
Since such reduced voltage is lower than the voltage at which the mass is pulled against its stops, there is a hysteresis in the force versus voltage curve.
While that article mentions that effective sensitivity increases with increasing electrode voltage, it also points out that the spring constant of the spring suspension system increases with increasing deflection. That article proposes improving damping by placing multiple channels into the structure while maximizing the electrode area, and notes that the effect therein disclosed allows for electronic tuning of the frequency response, concluding, however, that performance accuracy deteriorates when the deflection is not a small fraction of the gap, mentioning about 10% by way of example.
This confirms the prior-art opinion that operation of spring suspended sensor systems with a greatly reduced spring constant would introduce hysteresis and instability of operation, and would be undesirable. Also, various passive approaches attempted to deal with varying sensor sensitivity and even degraded performance for that reason.